[中學] 第一屆線上不等式競賽Day2
距離上次分享題目也隔了好長一段時間，中間有點太忙了。
最近應該會按一個禮拜一篇的速度分享這則競賽的題目。
由於次方在BBS上的表達比較困難，所以可能會以aa代替a平方,aaa代替a三次等
1st On-line Inequality Competition
October 26,2014 9:00 to 12:00(GMT+8)
Problem 4.
Let a1,...,an be the positive reals that satisfy a1a2...an=2^n. Prove that:
n-1 n-1 n-1
a1 a2 an
n + ------- + ------- + ... + ------- ≧ a1 + a2 + ... + an
n-1 n-1 n-1
a2 a3 a1
Problem 5.
Let a,b,c be positive reals satisfy aa + bb + cc = 1/3. Prove that:
a b c 3
---------- + ---------- + ---------- ≦ ---
√(a+bb) √(b+cc) √(c+aa) 2
Problem 6.
Let a,b,c be positive reals satisfy aa + bb + cc = 3. Prove that:
4(aaa+bbb+ccc) + 3(aabb+bbcc+ccaa) + 2abc≦23
出處：
https://www.facebook.com/profile.php?id=100004950046279
希望大家覺得這些題目有趣：）
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